Both phrases say essentially the same thing. The only thing is that we would not say "a difficulty." We might say "I'm having difficulty/difficulties" or get the best of both worlds with "I'm having a difficult time."

They mean the same thing. Another example: I am having a hard time learning Chinese = I am having difficulty learning Chinese. You can also say "I had a difficult time" doing something -- I am having a difficult time learning Chinese.

Thank you!

They mean the same thing, but if you say "difficulty" it will sound a little more mature than "a hard time." However, both phrases are completely acceptable and natural.